Final answer:
Grace Coolidge is the individual born on January 3, 1879, in Burlington, Vermont, who later became the First Lady of the United States.
Step-by-step explanation:
The person who was born on January 3, 1879, in Burlington, Vermont, is Grace Coolidge, the wife of Calvin Coolidge. Grace Coolidge became the First Lady of the United States when her husband, Calvin Coolidge, was elevated to the presidency upon the death of President Warren G. Harding in 1923. This brings to light the historical context surrounding the Coolidge presidency and his tenure at the White House.